1. Squares of Binomials
Chapter 5
Section 5.6

2. Objective
Students will find squares of binomials and factor perfect square trinomials

3. Vocabulary
Perfect square trinomial

4. Concept
A square of a binomial looks like (a + b)2. This means the same as (a + b)(a + b). The following slide explains a rule on how to solve a problem like this.

5. (a + b)2 = a2 + 2ab + b2 (a – b)2 = a2 – 2ab + b2
Concept
(a + b)2 = a2 + 2ab + b2 (a – b)2 = a2 – 2ab + b2

6. Concept
The expression on the right side of these equations are called perfect square trinomials because each expression has three terms and is the square of the binomial.

7. Example
(x + 3)2 (7u – 3)2

8. Example
(4s – 5t)2 (3p2 – 2q2)2

9. Concept
This pattern will also be useful for factoring. This means you will take a trinomial and determine whether it can be written as the square of binomials. a2 + 2ab + b2 = (a + b)2 a2 – 2ab + b2 = (a – b)2 To test whether a trinomial is a perfect square, ask yourself the following three questions.

10. Concept
1. Is the first term a square? 2. Is the last term a square? 3. Is the middle term, neglecting the sign, twice the sum of the product of the first term and last term?

11. Example
Decide whether a perfect square, then factor 4x2 – 20x u2 + 72uv + 81v2

12. Questions

13. Assignment
Worksheet